Search: id:A157659
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%I A157659
%S A157659 99,398,897,1596,2495,3594,4893,6392,8091,9990,12089,14388,16887,19586,
%T A157659 22485,25584,28883,32382,36081,39980,44079,48378,52877,57576,62475,
%U A157659 67574,72873,78372,84071,89970,96069,102368,108867,115566,122465,129564
%N A157659 a(n)=100*n^2-n (n>0)
%C A157659 If A=[A157659] 100*n.^2-n (99, 398, 897, 1596 ,..,); Y=[A157660] 8000*n-40 
               (7960, 15960, 23960..,); X=[A157661] 80000*n^2-800*n+1 (79201, 318401, 
               717601,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. 
               Example: 79201^2-99*7960^2=1; 318401^2-398*15960^2=1; 717601^2-897*23960^2=1.
%C A157659 If A=[A157659] 100*n.^2-n (99, 398, 897, ,.,); Y=[A010859] 20 (20, 20, 
               20,. ,.,); X=[A157955] 200*n-1 (199, 399, 599,. .,), we have, for 
               all terms, Pell's equation X^2-A*Y^2=1. Example: 199^2-99 *20^2=1; 
               399^2-398*20^2=1; 599^2-897*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 10 2009]
%H A157659 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A157659 Philippe Chevanne, <a href="http://mathafou.free.fr/themes/kpell.html">
               Pell Equation</a>
%H A157659 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&tstart=0">
               X^2-AY^2=1</a>
%F A157659 a(n)=100*n^2-n (n>0)
%e A157659 For n=1, a(1)=99; n=2, a(2)=398; n=3, a(3)=897
%Y A157659 Cf. A157660, A157661
%Y A157659 Cf. A010859, A157955 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 10 2009]
%Y A157659 Sequence in context: A008882 A156757 A027579 this_sequence A154359 A061366 
               A135219
%Y A157659 Adjacent sequences: A157656 A157657 A157658 this_sequence A157660 A157661 
               A157662
%K A157659 nonn
%O A157659 1,1
%A A157659 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 04 2009

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